Over the course of last summer we revised our standard “sophomore-level” differential equations course, taken by most engineering students. This is the course which traditionally has been a recipe course in which one learns to categorize all of the different types of differential equations which can be solved by hand while glossing over the fact that most differential equations can’t. The revision was to change it to be a more conceptual and more relevant course; in the following we look at some of the history of the course, the goals of the revision, and the outcome of our efforts.

### History

Our version of this course in the past appears to have been rooted in the traditional “recipe-driven” course, with evolutionary changes moving in the direction of a more conceptual, more demanding course. Resource constraints require that it be taught in a lecture of on the order of 100 students. The lecture meets three times a week for a standard 50 minute period. For very many years—since at least the mid-90s, and possibly earlier—there has been an extra hour a week associated with the course which has been in some weeks a computer lab and in others a standard recitation. The students in this course are 75–85% from the College of Engineering; the Department offers other courses in differential equations for other clientele (*e.g.*, a course that assumes that students have had a course in linear algebra and introduction to proof writing).

The original computer labs for the course were developed in the early to mid-90s and centered around Euler’s method and some applications; they underwent a major redesign in the late 1990s.[1] Those were the basis for the labs that were in use for the ensuing 10–15 years—let it not be said that our work does not have an ongoing impact! Between then and 2016, the labs evolved slowly, and largely in the direction of requiring less student knowledge of *Matlab* (the package used for the labs, as all engineering students at the University learn and use it) and, arguably, less conceptual engagement. Students had five sessions they spent working on the (5) labs, and the remaining weeks met in recitation, in which expected recitation type activities (question answering, material clarification) took place.

Common wisdom is that the course as it was before revision was perceived by students as easy and, as it was straightforward, a “good course.” An unscientific survey of student comments on ratemyprofessor.com[2] bears this out, finding it characterized as “the easiest of the required engineering math classes.”[3] Feedback on the labs in teaching evaluations suggested that students saw them as little more than hoops to jump through that didn’t connect to the course as a whole. Recitations, not surprisingly, were regarded as much more helpful. One might suppose that it’s difficult not to like a space where one is told the answers one seeks.

### Goals and Revision

At the end of the day, there is an increasing and persuasive body of evidence that indicates that if we are going to make a (mathematics) course effective, in the sense of engendering student learning, we must get students actively engaged with the material.[4,5,6] It is clear from the preceding discussion that the course was not necessarily doing a good job of this before its revision. Active engagement is difficult when the primary instruction takes place in a large lecture, and even the labs and recitations were not well structured to ensure active learning.